{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden"
   },
   "source": [
    "# Spectral Analysis of Deterministic Signals\n",
    "\n",
    "*This jupyter notebook is part of a [collection of notebooks](../index.ipynb) on various topics of Digital Signal Processing. Please direct questions and suggestions to [Sascha.Spors@uni-rostock.de](mailto:Sascha.Spors@uni-rostock.de).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Window Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the discussion of the leakage effect in the [previous section](leakage_effect.ipynb), a hard truncation of the signal $x[k]$ by a rectangular window $w[k] = \\text{rect}_N[k]$ was assumed. Also other window functions are used for spectral analysis. The resulting properties depend on the spectrum $W(\\mathrm{e}^{\\,\\mathrm{j}\\, \\Omega})$ of the window function, since the spectrum of the windowed signal is given by periodic convolution $X_N(\\mathrm{e}^{\\,\\mathrm{j}\\, \\Omega}) = \\frac{1}{2 \\pi} X(\\mathrm{e}^{\\,\\mathrm{j}\\, \\Omega}) \\circledast W(\\mathrm{e}^{\\,\\mathrm{j}\\, \\Omega})$. For an exponential signal $x[k] = \\mathrm{e}^{\\mathrm{j} \\Omega_0 k}$ this operation will result in a cyclic shift of the spectrum of the window function $W(\\mathrm{e}^{\\,\\mathrm{j}\\, \\Omega})$ by $\\Omega_0$.\n",
    "\n",
    "Different window functions have different properties. For instance with respect to the capability to distinguish two neighboring signals (frequency resolution) or to detect two signals when one is much weaker (sidelobe level). Since these two aspects counteract for typical window functions, the choice of a suitable window depends heavily on the application. First a look is taken at frequently applied window functions and their spectral properties. Then the window functions are compared by commonly used evaluation metrics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to investigate the windows, a function is defined which computes and plots the magnitude spectrum of a given window function. The discrete-time Fourier transform (DTFT) $W(\\mathrm{e}^{\\,\\mathrm{j}\\, \\Omega})$ is approximated numerically by the DFT."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.signal as sig\n",
    "\n",
    "\n",
    "def dft_window_function(w):\n",
    "    \n",
    "    N = len(w)\n",
    "    \n",
    "    # DFT of window function\n",
    "    W = np.fft.fft(w, 8192)\n",
    "    W = np.fft.fftshift(W)\n",
    "    W = W / np.amax(W) + np.nextafter(0,1)\n",
    "    mu = np.linspace(-np.pi, np.pi, 8192)\n",
    "\n",
    "    # plot window function and its spectrum\n",
    "    plt.rcParams['figure.figsize'] = 10, 5\n",
    "    plt.stem(w, basefmt=' ', use_line_collection=True)\n",
    "    plt.xlabel(r'$k$')\n",
    "    plt.ylabel(r'$w[k]$')\n",
    "    plt.axis([-1, N+1, -0.1, 1.1])\n",
    "    plt.grid()\n",
    "\n",
    "    plt.figure()\n",
    "    plt.plot(mu, 20*np.log10(np.abs(W)))\n",
    "    plt.xlabel(r'$\\Omega$')\n",
    "    plt.ylabel(r'$| W(e^{j \\Omega}) |$ in dB')\n",
    "    plt.axis([-np.pi, np.pi, -100, 5])\n",
    "    plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Rectangular Window"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The [rectangular window](https://en.wikipedia.org/wiki/Window_function#Rectangular_window) $w[k] = \\text{rect}_N[k]$ takes all samples with equal weight into account. The main lobe of its magnitude spectrum is narrow, but the level of the side lobes is rather high. It has the highest frequency selectivity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 960x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dft_window_function(np.ones(64))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Triangular Window"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For an odd window length $2N - 1$, the [triangular window](https://en.wikipedia.org/wiki/Window_function#Triangular_window) can be expressed as the convolution of two rectangular windows $w[k] = \\text{rect}_N[k] * \\text{rect}_N[k]$. The main lobe is wider than for the rectangular window, but the level of the side lobes decays faster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 960x480 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dft_window_function(sig.triang(63))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hanning Window"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The [Hanning window](https://en.wikipedia.org/wiki/Window_function#Hann_.28Hanning.29_window) $w[k] = \\frac{1}{2} ( 1 - \\cos(2 \\pi \\frac{k}{N}))$ is a smooth window whose first and last value is zero. It features a fast decay of the side lobes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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      ],
      "text/plain": [
       "<Figure size 960x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dft_window_function(np.hanning(64))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hamming Window"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The [Hamming window](https://en.wikipedia.org/wiki/Window_function#Hamming_window) $w[k] =  0.54 - 0.46 \\cos(2 \\pi \\frac{k}{N})$ is a smooth window function whose first and last value is not zero. The level of the side lobes is approximately constant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 960x480 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dft_window_function(np.hamming(64))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Blackman Window"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The [Blackman window](https://en.wikipedia.org/wiki/Window_function#Blackman_windows) $w[k] =  0.42 - 0.5 \\cos(2 \\pi \\frac{k}{N}) + 0.08 \\cos(4 \\pi \\frac{k}{N})$ features a rapid decay of side lobes at the cost of a wide main lobe and low frequency selectivity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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    }
   ],
   "source": [
    "dft_window_function(np.blackman(64))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparison of Window Functions\n",
    "\n",
    "Besides inspecting the DTFT of the window functions also various evaluation metrics are used for the comparison or selection of window functions. Three of the most prominent measures in spectral analysis are\n",
    "\n",
    "1. **Width of the main lobe**:\n",
    "The width of the main lobe in terms of normalized frequency is measured between the two points where its maximum value is dropped by half (- 3dB). This measure is linked to the capability to detect two exponential signals with comparable levels and similar frequencies.\n",
    "\n",
    "2. **Relative amplitude of side lobes**:\n",
    "Ratio in terms of amplitude between the maximum of the main lobe and the maximum level of the side lobes. This measure is linked to the detection performance when two or more exponential signals with disparate levels and dissimilar frequencies are present.\n",
    "\n",
    "3. **Maximum sampling error**:\n",
    "Maximum amplitude error when the maximum of the main lobe is not hit by sampling the spectrum. It is defined as the ratio between the amplitude of the main lobe and the amplitude at $\\Omega = \\frac{\\pi}{N}$. This measure provides insight into the maximum possible error when extracting the amplitude of harmonic signals from their DFT.\n",
    "\n",
    "The following table lists the values of these metrics for the introduced window functions:\n",
    "\n",
    "| window function | main lobe width | side lobe level | sampling error |\n",
    "|---|:---:|:---:|:---:|\n",
    "| [rectangular](#Rectangular-Window) | $\\frac{4 \\pi}{N + 1}$ | - 13 dB | 3.92 dB |\n",
    "| [triangular](#Triangular-Window) | $\\frac{8 \\pi}{N}$ | - 25 dB | 1.82 dB |\n",
    "| [Hanning](#Hanning-Window) | $\\frac{8 \\pi}{N}$ | - 31 dB | 1.42 dB |\n",
    "| [Hamming](#Hamming-Window) | $\\frac{8 \\pi}{N}$ | - 41 dB | 1.78 dB |\n",
    "| [Blackman](#Blackman-Window) | $\\frac{12 \\pi}{N}$ | - 57 dB | 1.10 dB |\n",
    "\n",
    "It is evident from the table that a lower side lobe level has a wider main lobe as consequence."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analysis of Signal Mixtures by the Windowed Discrete Fourier Transformation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The analysis of signal mixtures by the windowed DFT is illustrated by numerical examples. For this purpose, the function for the analysis of a [superposition of two exponential signals from the previous section](leakage_effect.ipynb#Analysis-of-signal-mixtures-by-the-discrete-Fourier-transformation) is extended by windowing the signal before taking its DFT."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dft_signal_mixture_window(N, A1, P1, A2, P2, w):\n",
    "    # N: length of signal/DFT\n",
    "    # A1, P1, A2, P2: amplitude and periodicity of 1st/2nd complex exponential\n",
    "    # window applied to the signal\n",
    "    \n",
    "    # generate the signal mixture\n",
    "    Om0_1 = P1*(2*np.pi/N)  # frequency of 1st exponential signal\n",
    "    Om0_2 = P2*(2*np.pi/N)  # frequency of 2nd exponential signal\n",
    "    k = np.arange(N)\n",
    "    x = A1 * np.exp(1j*Om0_1*k) + A2 * np.exp(1j*Om0_2*k)\n",
    "    x = x * w\n",
    "\n",
    "    # DFT of the signal mixture\n",
    "    mu = np.arange(N)\n",
    "    X = np.fft.fft(x)\n",
    "\n",
    "    # plot spectrum\n",
    "    plt.figure(figsize = (10, 8))\n",
    "    plt.stem(mu, abs(X), basefmt = ' ')\n",
    "    plt.title(r'Absolute value of the DFT of a signal mixture')\n",
    "    plt.xlabel(r'$\\mu$')\n",
    "    plt.ylabel(r'$|X[\\mu]|$')\n",
    "    plt.axis([0, N, -0.5, abs(X).max()+5])\n",
    "    plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the last example is re-investigated by using a Blackman window which features a high suppression of the sidelobes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/spors/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:19: UserWarning: In Matplotlib 3.3 individual lines on a stem plot will be added as a LineCollection instead of individual lines. This significantly improves the performance of a stem plot. To remove this warning and switch to the new behaviour, set the \"use_line_collection\" keyword argument to True.\n"
     ]
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5MCA4MzggNTAwIDUwMCA2MTMgNjM1IDU1MCA2MzUgNjE1IDM1MiA2MzUgNjM0IDI3OCAyNzggNTc5IDI3OCA5NzQgNjM0IDYxMgo2MzUgNjM1IDQxMSA1MjEgMzkyIDYzNCA1OTIgODE4IDU5MiA1OTIgNTI1IDYzNiAzMzcgNjM2IDgzOCA2MDAgNjM2IDYwMCAzMTgKMzUyIDUxOCAxMDAwIDUwMCA1MDAgNTAwIDEzNTAgNjM1IDQwMCAxMDcwIDYwMCA2ODUgNjAwIDYwMCAzMTggMzE4IDUxOCA1MTgKNTkwIDUwMCAxMDAwIDUwMCAxMDAwIDUyMSA0MDAgMTAyOCA2MDAgNTI1IDYxMSAzMTggNDAxIDYzNiA2MzYgNjM2IDYzNiAzMzcKNTAwIDUwMCAxMDAwIDQ3MSA2MTcgODM4IDM2MSAxMDAwIDUwMCA1MDAgODM4IDQwMSA0MDEgNTAwIDYzNiA2MzYgMzE4IDUwMAo0MDEgNDcxIDYxNyA5NjkgOTY5IDk2OSA1MzEgNjg0IDY4NCA2ODQgNjg0IDY4NCA2ODQgOTc0IDY5OCA2MzIgNjMyIDYzMiA2MzIKMjk1IDI5NSAyOTUgMjk1IDc3NSA3NDggNzg3IDc4NyA3ODcgNzg3IDc4NyA4MzggNzg3IDczMiA3MzIgNzMyIDczMiA2MTEgNjA4CjYzMCA2MTMgNjEzIDYxMyA2MTMgNjEzIDYxMyA5OTUgNTUwIDYxNSA2MTUgNjE1IDYxNSAyNzggMjc4IDI3OCAyNzggNjEyIDYzNAo2MTIgNjEyIDYxMiA2MTIgNjEyIDgzOCA2MTIgNjM0IDYzNCA2MzQgNjM0IDU5MiA2MzUgNTkyIF0KZW5kb2JqCjE2IDAgb2JqCjw8IC9YIDE3IDAgUiA+PgplbmRvYmoKMjMgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA4OCA+PgpzdHJlYW0KeJw1jLsNwDAIRHumuBH4OID3iVKR/dsQWy64e9IT5znAyD4PR+jELWRD4aZ4STmhPlE0Wm86tkhzv7xkMxcV/TPcfYXt5oBkNEnkIdHlcuVZKXo+l9obfgplbmRzdHJlYW0KZW5kb2JqCjI0IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTYwID4+CnN0cmVhbQp4nD2QSxLDIAxD95xCR8D4f550ukruv60NnWywGIT0wH1iIqMWJ4KvxIcGpcMk8GwVhHsw2RFyhOQETYaygyRxDQ0GpcKmY5nvyaZ10kqsvNF+2Xc0Zp10ii1Fh3Yh/+f1Ityj4BrrGTwPYDHI2kql7JkwWmWmrvKo6LUf0+E9D0SrxeX1Bq7w2kc3qSgqS+r+RHc02P6Rt/se3x+ZZTgkCmVuZHN0cmVhbQplbmRvYmoKMjUgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA3NCA+PgpzdHJlYW0KeJwzNTdVMFCwtAASpobmCuZGlgophlxAPoiVywUTywGzzEzMgCxDS2SWibEhkGViYYbEMjaxgMoiWAZAGmxNDsz0HK40AANxGJMKZW5kc3RyZWFtCmVuZG9iagoyNiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDY0ID4+CnN0cmVhbQp4nDMzNFQwUNA1AhJmhiYK5kaWCimGXEA+iJXLBRPLAbPMTMyALGNTUySWAZA2MjWD0xAZoAFwBkR/GgApTxROCmVuZHN0cmVhbQplbmRvYmoKMjcgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzMDQgPj4Kc3RyZWFtCnicPZI7ksMwDEN7nYIXyIz4k+TzZCeV9/7tPjLJVoBJiQAoL3WZsqY8IGkmCf/R4eFiO+V32J7NzMC1RC8TyynPoSvE3EX5spmNurI6xarDMJ1b9Kici4ZNk5rnKksZtwuew7WJ55Z9xA83NKgHdY1Lwg3d1WhZCs1wdf87vUfZdzU8F5tU6tQXjxdRFeb5IU+ih+lK4nw8KCFcezBGFhLkU9FAjrNcrfJeQvYOtxqywkFqSeezJzzYdXpPLm4XzRAPZLlU+E5R7O3QM77sSgk9ErbhWO59O5qx6RqbOOx+70bWyoyuaCF+yFcn6yVg3FMmRRJkTrZYbovVnu6hKKZzhnMZIOrZioZS5mJXq38MO28sL9ksyJTMCzJGp02eOHjIfo2a9HmV53j9AWzzczsKZW5kc3RyZWFtCmVuZG9iagoyOCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIzNyA+PgpzdHJlYW0KeJxFUUlyBCEMu/cr9IGpwivwnk7NqfP/aywzSU4WYGsxaYGBLXiJIdbAzIEvuXxN6DR8NzLb8DrZHnBPuC7cl8uCZ8KWwFdUl3e9L13ZSH13h6p+ZmR7s0jNkJWVOvVCNCbYIRE9IzLJVixzg6QprVLlvihbgC7qlbZOO42SoCMU4W+UI+HpFUp2TWwaq9Q6oKEIy7YuiDqZJKJ2YXFq8ZYhIp91YzXH+ItOInbH4/6sMOtRJJLSZwfdcSajTZZdAzm5eaqwVio5iD5e0caE6nSqgWO817b0E2ngufZf4Qc+ff+PGPq53j/G7lwiCmVuZHN0cmVhbQplbmRvYmoKMjkgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA1NCA+PgpzdHJlYW0KeJwzNjZXMFAwNDJX0DUyNlUwMjRQMDczUUgx5IIxc8EssGwOF1whhAmSz4GrzOFKAwBMkA8VCmVuZHN0cmVhbQplbmRvYmoKMzAgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA3MSA+PgpzdHJlYW0KeJwztjRQMFCwMFPQNTQ2VDCyNFYwNzNQSDHkAgqBWLlcMLEcMMvMEsQyNDdDYumaGUJlkVgg43K4YAbnwMzL4UoDAPG0FiMKZW5kc3RyZWFtCmVuZG9iagozMSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDY3ID4+CnN0cmVhbQp4nDO2NFAwULA0V9A1NDZUMDYwUTA3M1BIMeSCMXPBLLBsDhdMHYRlBmIYGZogscyAxoEl4QyQGTlw03K40gDOgxXTCmVuZHN0cmVhbQplbmRvYmoKMzIgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyNDUgPj4Kc3RyZWFtCnicRVC7jUMxDOs9BRcIYP0se553SJXbvz1KRnCFIVo/kloSmIjASwyxlG/iR0ZBPQu/F4XiM8TPF4VBzoSkQJz1GRCZeIbaRm7odnDOvMMzjDkCF8VacKbTmfZc2OScBycQzm2U8YxCuklUFXFUn3FM8aqyz43XgaW1bLPTkewhjYRLSSUml35TKv+0KVsq6NpFE7BI5IGTTTThLD9DkmLMoJRR9zC1jvRxspFHddDJ2Zw5LZnZ7qftTHwPWCaZUeUpnecyPiep81xOfe6zHdHkoqVV+5z93pGW8iK126HV6VclUZmN1aeQuDz/jJ/x/gOOoFk+CmVuZHN0cmVhbQplbmRvYmoKMzMgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzOTIgPj4Kc3RyZWFtCnicPVJLbgUxCNvPKbhApfBNcp6p3u7df1ubzFSqCi8DtjGUlwypJT/qkogzTH71cl3iUfK9bGpn5iHuLjam+FhyX7qG2HLRmmKxTxzJL8i0VFihVt2jQ/GFKBMPAC3ggQXhvhz/8ReowdewhXLDe2QCYErUbkDGQ9EZSFlBEWH7kRXopFCvbOHvKCBX1KyFoXRiiA2WACm+qw2JmKjZoIeElZKqHdLxjKTwW8FdiWFQW1vbBHhm0BDZ3pGNETPt0RlxWRFrPz3po1EytVEZD01nfPHdMlLz0RXopNLI3cpDZ89CJ2Ak5kmY53Aj4Z7bQQsx9HGvlk9s95gpVpHwBTvKAQO9/d6Sjc974CyMXNvsTCfw0WmnHBOtvh5i/YM/bEubXMcrh0UUqLwoCH7XQRNxfFjF92SjRHe0AdYjE9VoJRAMEsLO7TDyeMZ52d4VtOb0RGijRB7UjhE9KLLF5ZwVsKf8rM2xHJ4PJntvtI+UzMyohBXUdnqots9jHdR3nvv6/AEuAKEZCmVuZHN0cmVhbQplbmRvYmoKMzQgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxMzMgPj4Kc3RyZWFtCnicTY9BEsMwCAPvfoWegLEB8550ekr+fy2QNu4F7YyAkYYwCDxiDOswJbx6++FVpEtwNo75JRlFPAhqC9wXVAVHY4qd+Njdoeyl4ukUTYvrEXPTtKR0N1Eqbb2dyPjAfZ/eH1W2JJ2CHlvqhC7RJPJFAnPYVDDP6sZLS4+n7dneH2Y+M9cKZW5kc3RyZWFtCmVuZG9iagozNSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDI0NyA+PgpzdHJlYW0KeJxNUbttRDEM698UXOAA62t5ngtSXfZvQ8kIkMIgoS8ppyUW9sZLDOEHWw++5JFVQ38ePzHsMyw9yeTUP+a5yVQUvhWqm5hQF2Lh/WgEvBZ0LyIrygffj2UMc8734KMQl2AmNGCsb0kmF9W8M2TCiaGOw0GbVBh3TRQsrhXNM8jtVjeyOrMgbHglE+LGAEQE2ReQzWCjjLGVkMVyHqgKkgVaYNfpG1GLgiuU1gl0otbEuszgq+f2djdDL/LgqLp4fQzrS7DC6KV7LHyuQh/M9Ew7d0kjvfCmExFmDwVSmZ2RlTo9Yn23QP+fZSv4+8nP8/0LFShcKgplbmRzdHJlYW0KZW5kb2JqCjM2IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggOTAgPj4Kc3RyZWFtCnicTY1BEsAgCAPvvCJPUETQ/3R60v9fq9QOvcBOAokWRYL0NWpLMO64MhVrUCmYlJfAVTBcC9ruosr+MklMnYbTe7cDg7LxcYPSSfv2cXoAq/16Bt0P0hwiWAplbmRzdHJlYW0KZW5kb2JqCjM3IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMzM4ID4+CnN0cmVhbQp4nEVSS3LFMAjb5xRcIDPmZ+PzvE5X6f23lXA63Tz0DAgJMj1lSKbcNpZkhOQc8qVXZIjVkJ9GjkTEEN8pocCu8rm8lsRcyG6JSvGhHT+XpTcyza7QqrdHpzaLRjUrI+cgQ4R6VujM7lHbZMPrdiHpOlMWh3As/0MFspR1yimUBG1B39gj6G8WPBHcBrPmcrO5TG71v+5bC57XOluxbQdACZZz3mAGAMTDCdoAxNza3hYpKB9VuopJwq3yXCc7ULbQqnS8N4AZBxg5YMOSrQ7XaG8Awz4P9KJGxfYVoKgsIP7O2WbB3jHJSLAn5gZOPXE6xZFwSTjGAkCKreIUuvEd2OIvF66ImvAJdTplTbzCntrix0KTCO9ScQLwIhtuXR1FtWxP5wm0PyqSM2KkHsTRCZHUks4RFJcG9dAa+7iJGa+NxOaevt0/wjmf6/sXFriD4AplbmRzdHJlYW0KZW5kb2JqCjM4IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTYzID4+CnN0cmVhbQp4nEWQuXUEMQxDc1WBEniAOuoZP0ez/acLabzeQPp4hHiIPQnDcl3FhdENP962zDS8jjLcjfVlxviosUBO0AcYIhNXo0n17YozVOnh1WKuo6JcLzoiEsyS46tAI3w6ssdDW9uZfjqvf+wh7xP/KirnbmEBLqruQPlSH/HUj9lR6pqhjyorax5q2r8IuyKUtn1cTmWcunsHtMJnK1f7fQOo5zqACmVuZHN0cmVhbQplbmRvYmoKMzkgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA2OCA+PgpzdHJlYW0KeJwzMrdQMFCwNAEShhYmCuZmBgophlxAvqmJuUIuF0gMxMoBswyAtCWcgohbQjRBlIJYEKVmJmYQSTgDIpcGAMm0FeUKZW5kc3RyZWFtCmVuZG9iago0MCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDQ1ID4+CnN0cmVhbQp4nDMyt1AwULA0ARKGFiYK5mYGCimGXJYQVi4XTCwHzALRlnAKIp4GAJ99DLUKZW5kc3RyZWFtCmVuZG9iago0MSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDI1NSA+PgpzdHJlYW0KeJxFkUuSAyAIRPeegiOA/OQ8mZpVcv/tNJhMNnaXqP2ESiOmEiznFHkw/cjyzWS26bUcq52NAooiFMzkKvRYgdWdKeLMtUS19bEyctzpHYPiDeeunFSyuFHGOqo6FTim58r6qu78uCzKviOHMgVs1jkONnDltmGME6PNVneH+0SQp5Opo+J2kGz4g5PGvsrVFbhONvvqJRgHgn6hCUzyTaB1hkDj5il6cgn28XG780Cwt7wJpGwI5MgQjA5Bu06uf3Hr/N7/OsOd59oMV4538TtMa7vjLzHJirmARe4U1PM9F63rDB3vyZljctN9Q+dcsMvdQabP/B/r9w9QimaICmVuZHN0cmVhbQplbmRvYmoKNDIgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxNjEgPj4Kc3RyZWFtCnicRZBLEsMgDEP3nEJH8EcGfJ50ukrvv60hTbOAp7FABncnBKm1BRPRBS9tS7oLPlsJzsZ46DZuNRLkBHWAVqTjaJRSfbnFaZV08Wg2cysLrRMdZg56lKMZoBA6Fd7touRypu7O+Udw9V/1R7HunM3EwGTlDoRm9SnufJsdUV3dZH/SY27Wa38V9qqwtKyl5YTbzl0zoATuqRzt/QWpczqECmVuZHN0cmVhbQplbmRvYmoKNDMgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyMTQgPj4Kc3RyZWFtCnicPVC7EUMxCOs9BQvkznztN8/Lpcv+bSScpEI2QhKUmkzJlIc6ypKsKU8dPktih7yH5W5kNiUqRS+TsCX30ArxfYnmFPfd1ZazQzSXaDl+CzMqqhsd00s2mnAqE7qg3MMz+g1tdANWhx6xWyDQpGDXtiByxw8YDMGZE4siDEpNBv+tcvdS3O89HG+iiJR08K755fTLzy28Tj2ORLq9+YprcaY6CkRwRmryinRhxbLIQ6TVBDU9A2u1AK7eevk3aEd0GYDsE4njNKUcQ//WuMfrA4eKUvQKZW5kc3RyZWFtCmVuZG9iago0NCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDgwID4+CnN0cmVhbQp4nEWMuw3AMAhEe6ZgBH4mZp8olbN/GyBK3HBPunu4OhIyU95hhocEngwshlPxBpmjYDW4RlKNneyjsG5fdYHmelOr9fcHKk92dnE9zcsZ9AplbmRzdHJlYW0KZW5kb2JqCjQ1IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTU3ID4+CnN0cmVhbQp4nEWQuRFDMQhEc1VBCRKwCOqxx9F3/6kX+Uq0bwAth68lU6ofJyKm3Ndo9DB5Dp9NJVYs2Ca2kxpyGxZBSjGYeE4xq6O3oZmH1Ou4qKq4dWaV02nLysV/82hXM5M9wjXqJ/BN6PifPLSp6FugrwuUfUC1OJ1JUDF9r2KBo5x2fyKcGOA+GUeZKSNxYm4K7PcZAGa+V7jG4wXdATd5CmVuZHN0cmVhbQplbmRvYmoKNDYgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzMzIgPj4Kc3RyZWFtCnicLVI5jiQxDMv9Cn5gAOvy8Z4eTNT7/3RJVQUFqmzLPORyw0QlfiyQ21Fr4tdGZqDC8K+rzIXvSNvIOohryEVcyZbCZ0Qs5DHEPMSC79v4GR75rMzJswfGL9n3GVbsqQnLQsaLM7TDKo7DKsixYOsiqnt4U6TDqSTY44v/PsVzF4IWviNowC/556sjeL6kRdo9Ztu0Ww+WaUeVFJaD7WnOy+RL6yxXx+P5INneFTtCaleAojB3xnkujjJtZURrYWeDpMbF9ubYj6UEXejGZaQ4AvmZKsIDSprMbKIg/sjpIacyEKau6Uont1EVd+rJXLO5vJ1JMlv3RYrNFM7rwpn1d5gyq807eZYTpU5F+Bl7tgQNnePq2WuZhUa3OcErJXw2dnpy8r2aWQ/JqUhIFdO6Ck6jyBRL2Jb4moqa0tTL8N+X9xl//wEz4nwBCmVuZHN0cmVhbQplbmRvYmoKNDcgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzMTcgPj4Kc3RyZWFtCnicNVJLckMxCNu/U3CBzpi/fZ50smruv62EJyuwLUBCLi9Z0kt+1CXbpcPkVx/3JbFCPo/tmsxSxfcWsxTPLa9HzxG3LQoEURM9+DInFSLUz9ToOnhhlz4DrxBOKRZ4B5MABq/hX3iUToPAOxsy3hGTkRoQJMGaS4tNSJQ9Sfwr5fWklTR0fiYrc/l7cqkUaqPJCBUgWLnYB6QrKR4kEz2JSLJyvTdWiN6QV5LHZyUmGRDdJrFNtMDj3JW0hJmYQgXmWIDVdLO6+hxMWOOwhPEqYRbVg02eNamEZrSOY2TDePfCTImFhsMSUJt9lQmql4/T3AkjpkdNdu3Csls27yFEo/kzLJTBxygkAYdOYyQK0rCAEYE5vbCKveYLORbAiGWdmiwMbWglu3qOhcDQnLOlYcbXntfz/gdFW3ujCmVuZHN0cmVhbQplbmRvYmoKNDggMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxNyA+PgpzdHJlYW0KeJwzNrRQMIDDFEMuABqUAuwKZW5kc3RyZWFtCmVuZG9iago0OSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDEzMSA+PgpzdHJlYW0KeJxFj8sNBCEMQ+9U4RLyGT6ph9We2P6v6zCaQUL4QSI78TAIrPPyNtDF8NGiwzf+NtWrY5UsH7p6UlYP6ZCHvPIVUGkwUcSFWUwdQ2HOmMrIljK3G+G2TYOsbJVUrYN2PAYPtqdlqwh+qW1h6izxDMJVXrjHDT+QS613vVW+f0JTMJcKZW5kc3RyZWFtCmVuZG9iago1MCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDMzOCA+PgpzdHJlYW0KeJw1Ujmu3UAM630KXSCAds2c5wWpfu7fhpRfCkO0VoqajhaVafllIVUtky6/7UltiRvy98kKiROSVyXapQyRUPk8hVS/Z8u8vtacESBLlQqTk5LHJQv+DJfeLhznY2s/jyN3PXpgVYyEEgHLFBOja1k6u8Oajfw8pgE/4hFyrli3HGMVSA26cdoV70PzecgaIGaYlooKXVaJFn5B8aBHrX33WFRYINHtHElwjI1QkYB2gdpIDDmzFruoL/pZlJgJdO2LIu6iwBJJzJxiXTr6Dz50LKi/NuPLr45K+kgra0zad6NJacwik66XRW83b309uEDzLsp/Xs0gQVPWKGl80KqdYyiaGWWFdxyaDDTHHIfMEzyHMxKU9H0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    "The second exponential signal with the lower level now becomes visible in the spectrum."
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   "source": [
    "**Exercise**\n",
    "\n",
    "* Examine the effect of the other window functions for small/large frequency and level differences. What window function is best suited for what situation?\n",
    "\n",
    "Solution: The rectangular window function is well suited to identify two or more exponential signals with comparable amplitudes and only minor differences in frequency. This is due to its narrow main lobe. Window functions that feature a higher decay of the side lobes are well suited for the identification of exponential signals with rather different levels and frequencies."
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    "**Copyright**\n",
    "\n",
    "This notebook is provided as [Open Educational Resource](https://en.wikipedia.org/wiki/Open_educational_resources). Feel free to use the notebook for your own purposes. The text is licensed under [Creative Commons Attribution 4.0](https://creativecommons.org/licenses/by/4.0/), the code of the IPython examples under the [MIT license](https://opensource.org/licenses/MIT). Please attribute the work as follows: *Sascha Spors, Digital Signal Processing - Lecture notes featuring computational examples*."
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